Affine Deligne–Lusztig varieties and quantum Bruhat graph - Sadhukhan, Arghya (Mathematische Zeitschrift, 2023)
In this paper, we consider affine Deligne–Lusztig varieties X w ( b ) and their certain union X ( μ , b ) inside the affine flag variety of a reductive group. Several important results in the study of affine Deligne–Lusztig varieties have been established under the so-called superregularity hypothesis. Such results include a description of generic Newton points in Iwahori double cosets of loop groups, covering relation in the associated Iwahori–Weyl group and a dimension formula for X ( μ , b ) . We show that one can considerably weaken the superregularity hypothesis and sometimes eliminate it, thus strengthening these existing results.